Question

a side of the triangle below has been extended to form an exterior angle of 137°. find the value of x.

Explanation:

Step1: Use the exterior angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior angle is \(137^{\circ}\), and the two non - adjacent interior angles are \(x^{\circ}\) and \(90^{\circ}\). So, we have the equation \(x + 90=137\).

Step2: Solve for \(x\)

Subtract \(90\) from both sides of the equation \(x + 90=137\). Using the subtraction property of equality: \(x=137 - 90\).

Answer:

\(x = 47\)